QUESTION 3 (25 Marks)
INFORMATION
Avery Manufacturers intends purchasing a new machine and has a choice between two
machines viz. Machine A or Machine B. The cost of each machine is R3 000 000, with each
having an expected useful life of five years. Machine A is expected to have a scrap value of
R200 000. No scrap value is expected for Machine B. Avery Manufacturers uses the
straight-line method of deprecation. The cost of capital is estimated at 16%.
Machine A is expected to generate the following net profits over its useful life: Year 1 R340
000
Year 2 R280 000
Year 3 R550 000
Year 4 R340 000
Year 5 R160 000
Machine B is expected to generate a net profit of R340 000 per year over the five-year
period. Ignore taxes.
REQUIRED
Answer the questions based on the information supplied.
Use the information provided below to calculate the following. Where applicable, use the four-
decimal present value tables provided in APPENDICES 1 and 2
3.1 Accounting Rate of Return (on initial investment) of Machine A (expressed to two
decimal places) (5)
3.2 Net Present Value of each machine (8)
3. 3 Internal Rate of Return of Machine B (expressed to two decimal places) using
interpolation. (7)
3.4 Payback period for of Machine A (5)
3.1 The Accounting Rate of Return (ARR) of Machine A can be calculated as follows:
Average Annual Profit = (Total Net Profit / Useful Life) = (340,000 + 280,000 + 550,000 + 340,000 + 160,000) / 5 = 334,000
Accounting Rate of Return = (Average Annual Profit / Initial Investment) x 100% = (334,000 / 3,000,000) x 100% = 11.13%
Therefore, the Accounting Rate of Return of Machine A is 11.13%.
3.2 The Net Present Value (NPV) of each machine can be calculated as follows:
NPV = Cash Inflows - Initial Investment - Present Value of Salvage Value (if any)
For Machine A:
NPV(A) = 340,000/(1+0.16)^1 + 280,000/(1+0.16)^2 + 550,000/(1+0.16)^3 + 340,000/(1+0.16)^4 + 160,000/(1+0.16)^5 - 3,000,000 - 200,000/(1+0.16)^5
NPV(A) = 294,827.59 + 227,899.94 + 385,903.85 + 192,728.30 + 74,703.47 - 3,000,000 - 129,449.60
NPV(A) = 47,613.55
For Machine B:
NPV(B) = 340,000/(1+0.16)^1 + 340,000/(1+0.16)^2 + 340,000/(1+0.16)^3 + 340,000/(1+0.16)^4 + 340,000/(1+0.16)^5 - 3,000,000
NPV(B) = 293,103.45 + 252,638.88 + 217,792.22 + 187,520.19 + 161,391.40 - 3,000,000
NPV(B) = 112,446.14
Therefore, the Net Present Value of Machine A is R47,613.55 and Machine B is R112,446.14.
3.3 To calculate the Internal Rate of Return (IRR) of Machine B using interpolation:
IRR(B) = Lower Rate + (NPV at Lower Rate / (NPV at Lower Rate - NPV at Higher Rate)) x (Higher Rate - Lower Rate)
NPV at 15% = 112,446.14 (from previous calculation)
NPV at 20% = 112,446.14 (calculation required)
Using the present value tables, the NPV at 20% can be calculated as:
NPV(B) at 20% = 340,000/(1+0.20)^1 + 340,000/(1+0.20)^2 + 340,000/(1+0.20)^3 + 340,000/(1+0.20)^4 + 340,000/(1+0.20)^5 - 3,000,000
NPV(B) at 20% = 283,333.33 + 236,111.11 + 196,759.26 + 163,966.05 + 136,638.37 - 3,000,000
NPV(B) at 20% = 16,808.12
IRR(B) = 15% + (112,446.14 / (112,446.14 - 16,808.12)) x (20% - 15%)
IRR(B) = 17.6895%
Therefore, the Internal Rate of Return of Machine B using interpolation is approximately 17.69%.
3.4 The Payback Period for Machine A can be calculated by determining the time it takes to recover the initial investment:
Cumulative Cash Inflows:
Year 1: 340,000
Year 2: 340,000 + 280,000 = 620,000
Year 3: 620,000 + 550,000 = 1,170,000
Year 4: 1,170,000 + 340,000 = 1,510,000
Year 5: 1,510,000 + 160,000 = 1,670,000
Payback Period for Machine A:
3 years + (3,000,000 - 1,170,000) / 340,000 = 3 years + 1.7941 years = 4.7941 years
Therefore, the Payback Period for Machine A is approximately 4.79 years.